Cloth is an important material to model and simulate correctly, both in computer graphics and other industrial applications. The commonly used models for cloth in computer graphics typically approximate the cloth as an elastic sheet with linear isotropic behavior inspired by the construction of woven fabrics. However, they do a poor job of predicting the behavior of knits, which are driven by the complex interactions of yarn loops pulled through each other. This thesis presents a yarn-based model for cloth where yarns in the fabric are explicitly modeled as inextensible but flexible spline curves. Yarn dynamics are dictated by both energy terms and hard constraints, while friction interactions, a critical component of correct yarn behavior, are approximated using a velocity filter that penalizes locally non-rigid motion. Qualitative comparison of the model to observed deformations of hand-knitted samples in the laboratory showed that the model predicts key mechanical properties of different knits. Since this model is slower than sheet-based approaches, further work looked at accelerating the model through both localized rigidification and adaptive contact linearization. In localized rigidification, regions of the cloth behaving almost rigidly are simulated using a cheaper model which avoids many of the expensive force computations. For adaptive contact linearization, yarn contacts are grouped into contact sets, with the associated contact force computed exactly at one timestep, and then approximated on subsequent steps via linearization in a rotated reference frame for nearby geometric configurations. Finally, additional work looked at the problem of creating initial yarn geometry for subsequent simulation as a yarn-based model.